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WASHINGTON — To the relief of the British public and taffeta-craving masses elsewhere, Prince William announced yesterday that he is officially engaged.

He proposed to his longtime girlfriend, Kate Middleton, while on vacation in Kenya a few weeks ago, according to a statement issued by palace officials. A wedding is planned for the spring or summer of 2011. Other details were meted out, most notably that the engagement ring presented to Middleton, a brilliant oval sapphire surrounded with smaller diamonds, had once belonged to William’s late mother, Diana. “It was my way of keeping her close to it all,’’ William said in the couple’s first television interview on BBC.

The symbolism awakened a faint flutter of hope: The era of Diana has returned.

William’s nuptials will probably be Britain’s grandest royal wedding in nearly 30 years. But more than that, the young lovers represent a royal redemption from the fraught triangle of Charles and Diana and Camilla. Over the past two decades, the reputation of the entire royal family has steadily declined from regal to rancid. There was the divorce of Charles’s brother, Andrew, not to mention further drama earlier this year when his former wife, the Duchess of York (“Fergie’’), was caught on video arranging payment for access to her ex.

Queen Elizabeth II, herself besieged by a burnt palace and a tax scandal, and portrayed in a 2007 biopic as kind of a jerk, once declared 1992 as her “annus horribilis.’’

It is now up to William to transform 2011 into an annus mirabilis.

“It’s great to have a piece of unadulterated good news that everyone can celebrate,’’ jubilant Prime Minister David Cameron told his equally jubilant Cabinet. “I’m sure this is something [that will see] the country come together.’’

“I think the monarchy has really fallen in tattered times,’’ said Kitty Kelley, the biographer and chronicler of the Diana-era monarchy in “The Royals.’’ “There is a movement afoot to really run the monarchy out’’ after the death of Queen Elizabeth. A royal wedding of this magnitude, Kelley said, makes the whole family look good.

In England, Londoners received the news with relief, as if already looking beyond the Charles years that have not even begun. “It’s lovely to see a member of the royal family marrying someone who is down to earth, someone you can relate to,’’ said Natalie Varney, a graduate student. “The younger generation will get more interested in the royal family.’’

The couple met in 2001, studying at the University of St. Andrews — geography for him, art history for her — in a coastal Scottish town with castle ruins and cobblestone walks. They lived in a group house, just friends, they said, until suddenly they became more. The “more’’ was rumored to happen when Kate was strutting the catwalk in lingerie for a student fashion show.

Her wealthy parents made their money in a party-planning business; her mother had once been a flight attendant. The lingerie, the friendly skies — all of it together prompted some in the public to question whether the prince’s commoner girlfriend was fit to marry their Wills, about whom the nation has come to feel protective.

The media derisively dubbed her “Middleclass Middleton.’’

But gradually Middleton began to appear at public events, smiling graciously and consistently on William’s arm and wearing the enormous froufrou hats required of British swells, with far more aplomb than could be expected from a recent college grad.

Yesterday the couple, both 28, sat for their first public interview, Kate in a snug, plunging-neckline dress that perfectly matched the sapphire on her hand.

“I’d been carrying it around in my rucksack for months,’’ William said of the ring, gamely playing the part of the guy who didn’t know if she’d even say yes.

Asked why it took him so long to propose, William said, half-seriously, “I wanted to give her a chance’’ to witness the incredible pressure of living in a fishbowl and, if she didn’t think she could handle it, “to back out.’’

The office of the prince has not announced further details of the wedding. There was speculation that the date was set for 2011 so as not to interfere with London’s Summer Olympics hosting duties in 2012.

When Charles and Diana were interviewed shortly after their engagement, a reporter famously asked if they were in love. A glowing Diana demurely replied, “Of course.’’ But Charles dismissively snarked: “Whatever love is.’’

The same question was not posed to William and Kate Middleton yesterday. Britain has grown wiser, perhaps, in the past 30 years, knowing to avoid questions with potentially awkward answers.